Approximation Algorithms for D-optimal Design

• 成果类型: Article
• 署名作者: Singh, Mohit; Xie, Weijun
• 署名单位: University System of Georgia; Georgia Institute of Technology; Virginia Polytechnic Institute & State University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2019.1041
• 发表日期: 2020
• 页码: 1512-1534

摘要

Experimental design is a classical statistics problem, and its aim is to estimate an unknown vector from linear measurements where a Gaussian noise is introduced in each measurement. For the combinatorial experimental design problem, the goal is to pick a subset of experiments so as to make the most accurate estimate of the unknown parameters. In this paper, we will study one of the most robust measures of error estimation-the D-optimality criterion, which corresponds to minimizing the volume of the confidence ellipsoid for the estimation error. The problemgives rise to two natural variants depending on whether repetitions of experiments are allowed or not. We first propose an approximation algorithm with a 1/e-approximation for the D-optimal design problem with and without repetitions, giving the first constant-factor approximation for the problem. We then analyze another sampling approximation algorithmand prove that it is asymptotically optimal. Finally, for D-optimal design with repetitions, we study a different algorithm proposed by the literature and show that it can improve this asymptotic approximation ratio. All the sampling algorithms studied in this paper are shown to admit polynomial-time deterministic implementations.